One clear afternoon last December, in a tall, red-brick building off the King’s Road in London, four old rockers sat aimlessly in a recording studio.

They had already spent two days waiting and wondering when — and if — their lead singer and most famous member was going to appear.

Keith Richards set up the sessions, ostensibly to provide some material for a TV documentary about the Rolling Stones to celebrate their 50th anniversary, which falls next month.

All over now: Keith Richards, left, and Mick Jagger appear to still have a long way to go to patch up their differences

But in fact, the sessions were an attempt to reconnect with his old friend Mick Jagger.

Keith — who lives mostly in Connecticut these days — turned up on day one, as did lugubrious drummer Charlie Watts and guitarist Ronnie Wood, who is keen to reunite the Stones. Rather surprisingly Bill Wyman, looking as gloomy ever with a chestnut mullet, was also back on bass guitar.

It has been 20 years since he left the band amid the Mandy Smith scandal after having seduced the 13-year-old schoolgirl who went on to become his wife, but Keith said that he had missed Wyman, with whom he has had scant contact in the intervening years, and was pleased to see him.

However, Mick Jagger kept them all hanging before he deigned to show up — on day three.

Revealed: Keith Richards, pictured with his biography, which didn't help his relationship with Mick Jagger

And when he did, he made no commitment to the idea of repeating the experience. I’m told he was polite and professional — but returned to his home in Chelsea the minute the cameras stopped rolling.

In an interview this week in Rolling Stone magazine, Keith tried to put the best possible gloss on matters. He said: ‘On the third day, Mick turned up, which was a real joy. Because I set it up really as a magnet, you know.’

He previously admitted that he had no idea whether Mick would feel able to come.

In November last year he said: ‘My basic thing is that Ronnie, Charlie and I are going to work together. Just go in and see if we can warm our chops up. And of course everyone else is welcome. [Guitarist] Mick Taylor’s welcome. I don’t see why everybody who was a Stone shouldn’t be involved.’

However, I can reveal that despite this faux friendliness put on for a media blitz this week, and claims that a money-spinning world tour are on hold because of fears about Keith’s health, relations between he and Jagger remain positively arctic — despite many efforts to patch them up.

Keith almost died in 2006 after falling out of a tree while on holiday in Fiji and suffering a brain haemorrhage and there were suggestions this week that his health is too poor to withstand the rigours of touring.

But several sources insist the real problem is the animosity between him and Mick — and that it could finish the Stones for good.

One source says: ‘They are trying very hard to put across the image that they are all pals and that it is forgotten, but it is still a completely dysfunctional and broken relationship.’

Still talking: Mick Jagger and guitarist Ron Wood on stage during the Rolling Stones' 1975 Tour of the Americas

The band was forced to admit this week that they will not be ‘ready’ for a tour for their 50th anniversary this year. Keith, however, says that he has hopes that they might manage it in 2013. There are tentative plans to get together again in New York to work on new material in the coming months, but nobody is sure whether Mick will actually show up.

In truth, Mick and Keith, both 68, can only just bear to share a room. They don’t speak — and have barely done so in 20 years. Keith pulled out of one of their last public appearances — in Cannes in 2010 to promote a Stones documentary — as he felt the movie was more about Mick than him.

A source says: ‘They are incredibly petty with each other, and gripe over small things continuously. Keith gets really annoyed that Mick always goes on stage last for instance. It winds him up terribly, and has done for years.’

By way of revenge, Keith calls Mick ‘Brenda’ (borrowing Private Eye’s nickname for the Queen), ‘Miss Jagger,’ and ‘Her Ladyship’ — and for years has mocked his distinctive dancing and prancing.

Fallout: It seems these days it's a challenge just to get Jagger and Richards to be in the same room

I’m told that, in recent months, their respective lawyers and managers have had many meetings, costing thousands of pounds, hoping to put a tour together. But so far the Rolling Stones have only managed to agree on the release of an authorised book, a greatest hits boxed set of CDs and the television documentary.

Keith, however, wants to regroup for a final tour to go out with a bang.One pal says: ‘There may be a day or two after coming off a two-year tour when Keith doesn’t want to play, but aside from that he wakes up every day and wants to get on stage.’

Ronnie, meanwhile, could do with the money after last year’s expensive divorce from his wife, Jo. Charlie Watts has said he will tour. But Mick has yet to say yes.

Affair: Richards admitted he had an affair with Jagger's girlfriend at the time Marianne Faithfull, pictured here

The current elephant in the room, if that is not too unfortunate a phrase in the circumstances, is what Keith said about Mick’s membrum virile in 2010.

He accused his old friend of having a ‘tiny todger’ — and went on to claim he had enjoyed an affair with Mick’s girlfriend Marianne Faithfull in 1960, delightedly exclaiming at his good fortune in burying his head in her ‘beautiful jugs’ during an afternoon sex session.

The claims, made in his autobiography, Life, were astonishing.

It wasn’t so much the liaison with Marianne — at around this time there was rather a sexual merry-go-round when it came to women. (For instance rock chick Anita Pallenberg was the girlfriend of late Rolling Stones member Brian Jones, then took up with Keith, then had a fling with Mick — before going back to Keith again.)

What really amazed everyone was the casual way Keith chose to spread such a damaging and deeply personal slur about Mick, who has long gloried in his reputation as the ultimate womaniser.

One source intimately connected with the band tells me that the relationship between the pair is the fundamental reason why the Stones have been dormant since the end of their last tour, A Bigger Bang, in 2007.

The source says: ‘Mick and Keith have not got over ‘willygate’. Mick feels that Keith violated their friendship completely, damaged his reputation and that of the Rolling Stones.

In public at least, Keith has been prevailed upon to apologise. He said of Jagger this week: ‘He and I have had conversations over the past year of a kind we have not had for an extremely long time, and that has been incredibly important to me.

‘As far as the book goes, it was my story and it was very raw, as I meant it to be. But I know that some parts of it, and some of the publicity, really offended Mick and I regret that.’

Will that be enough to allow them to put the enmity behind them Many Stones-watchers doubt that it will. Mick’s carefully crafted response to Keith’s grovel was measured, but had a certain patronising chilliness.

He replied: ‘Looking back at any career you are bound to recall both the highs and the lows. In the Eighties, Keith and I were not communicating very well. I got very involved with the business side of the Stones, mainly because I felt no one else was interested. But it’s plain now from the book that Keith felt excluded, which is a pity. Time, I reckon, to move on.’

Notice he felt unable to address the offence which Keith caused with his book, such is his revulsion for the row. Instead, he forgives him for the rows which they had 30 years ago.

Here's hoping: Ronnie Wood hopes it can all come good for a Rolling Stones reunion

The two rockers — who met at primary school in Dartford in 1951 — have weathered drugs busts, scandals and band members coming and going, but their relationship has always been tense. Listen to Gimme Shelter, which Keith begun writing while waiting for faithless Anita to return to his bed from Mick’s, and the pain is evident.

In the Seventies, obvious cracks began to appear. Keith felt Mick had sold out on rock music. Mick, felt that Keith — deeply addicted to heroin — was out of control.

By the Eighties, Jagger was detached enough to make a solo album, She’s The Boss. Keith was furious and even tried to get The Who’s Roger Daltrey to replace Mick in the band’s line-up. The recording of the band’s album Dirty Work, in Paris in 1985, was fraught: studio time was organised so that Mick and Keith wouldn’t have to be in the same room at the same time.

Ronnie Wood effected a truce in 1987. But Keith just couldn’t resist winding up his old friend in the years that followed. He said Mick was vain and belonged in panto. He criticised his womanising. Last year, he dismissed Mick’s solo album Goddess In The Doorway as ‘Dogs**t In The Doorway’. It has always been one dig after another. They seem to enjoy being best of enemies.

They are, of course, very different people. As a friend puts it: ‘Mick has lots of interests, but Keith just has his guitar. Keith will carry on playing whether it’s with the Stones or with someone else.’

‘He is quite erratic these days, which may be a result of his fall,’ the source says. ‘His standard response to most conversational gambits is to growl: “It’s a chemical thing, man.” He likes to play up his druggie image, which you don’t get with Mick.’

The Stones source adds that Keith broke the Stones’ ‘sacred agreement’ that you can bicker all you like, but you don’t air your dirty laundry in public.

Top trio: Charlie Watts, Mick Jagger and Keith Richards – can a tour ever be a possibility

By contrast, Mick has always turned down offers to write his autobiography, claiming he couldn’t remember enough about the Stones’ early days. Actually, it is said he simply prefers not to reveal too much about them — a little mystery is always lucrative.

So where does all this leave them

Ronnie Wood hopes it will all come good. Charlie Watts has long been the peacemaker in the group but now refuses to intervene in the bickering.

Keith Well, he knows he crossed the line, but seems to believe he will be forgiven. But one of Mick’s pals insists a tour will ‘never’ happen as, apology or not, Mick still cannot stand Keith.

He says the likely outcome is a one-off filmed concert, which will be sold across the world. Others believe they will eventually do a tour — for the money if nothing else. Someone who has spoken to the band in the past few weeks says: ‘Mick likes to make money, and Keith likes to play. And they do both believe they are the greatest band on earth and should go out with a bang.’